I. Field of the Invention
The present invention relates to a method for approximating optimal control variables of a nonlinear discrete time system.
II. Description of Related Art
The use of neural networks simulated by one or more processors has enjoyed increased popularity for the control of discrete nonlinear time systems. Such neural networks are defined by a plurality of nodes having one or more inputs and one or more outputs. In recurrent neural networks, at least one of the outputs forms a feedback input to the network.
In order to obtain the appropriate weights for each of the nodes in the neural network, it has been previously necessary to train the neural network using conventional training techniques. These techniques include, for example, applying known or desired state variables and training the network to produce known or desired outputs.
One disadvantage to recurrent neural networks, however, is that, due to the feedback inherent in a recurrent neural network, training of the neural network provides feedback/parameterized solutions for the network in which the control variables are necessarily dependent on each other. This, however, oftentimes results in solutions for the neural network having local minima. Such local minima, of course, are undesirable and detract from the overall operation of the neural network.